Compute matrix trace and support updates

Q: Compute matrix trace and support updates

This question evaluates proficiency in matrix manipulation, incremental updates, and complexity analysis, specifically maintaining main-diagonal and anti-diagonal sums under point updates.

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Question

Given an n x n integer matrix M, implement a function trace (M) that returns the sum of its main diagonal. Follow-ups: (a) If you receive q point updates (i, j, val) changing M[i][j] to val, design a data structure to return the current trace after each update in O(

time; (b) Extend the function to also compute the anti-diagonal sum efficiently; (c) Discuss time and space complexities and edge cases (non-square input, large n).

Compute matrix trace and support updates

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